scholarly journals Wave Response during Hydrostatic and Geostrophic Adjustment. Part II: Potential Vorticity Conservation and Energy Partitioning

2005 ◽  
Vol 62 (5) ◽  
pp. 1330-1345 ◽  
Author(s):  
Jeffrey M. Chagnon ◽  
Peter R. Bannon
Keyword(s):  
Steady State ◽  
Potential Vorticity ◽  
Acoustic Waves ◽  
High Frequency ◽  
Lamb Waves ◽  
Geostrophic Adjustment ◽  
Horizontal Scale ◽  
Extended Duration ◽  
High Frequency Waves ◽  
Buoyancy Waves

Abstract This second part of a two-part study of the hydrostatic and geostrophic adjustment examines the potential vorticity and energetics of the acoustic waves, buoyancy waves, Lamb waves, and steady state that are generated following the prescribed injection of heat into an isothermal atmosphere at rest. The potential vorticity is only nonzero for the steady class and depends only on the spatial and time-integrated properties of the injection. The waves contain zero net potential vorticity, but undergo a time-dependent vorticity exchange involving latent and relative vorticities. The energy associated with a given injection may be partitioned distinctly among the various wave classes. The characteristics of this partitioning depend on the spatiotemporal detail of the injection, as well as whether the imbalance is generated by injection of heat, mass, or momentum. Spatially, waves of a scale similar to that of the injection are preferentially excited. Temporally, an extended duration injection preferentially filters high-frequency waves. An instantaneous injection, that is, the temporal Green’s function, contains the largest proportions of the high-frequency waves. The proportions of kinetic, available elastic, and available potential energies that are carried by the various waves are functions of the homogeneous system. For example, deep buoyancy waves of small horizontal scale primarily contain equal portions of available potential and vertical kinetic energy. The steady state contains more available potential energy than kinetic energy at small horizontal scale, and vice versa. These qualities of the wave energetics illustrate the mechanisms that characterize the physics of each wave class. The evolution and spectral partitioning of the energetics following localized warmings identical to those in Part I are presented in order to illustrate some of these basic properties of the energetics. For example, a heating lasting longer than a few minutes does not excite acoustic waves. However, Lamb waves of wide horizontal scale can be excited by a heating of several hours. The first buoyancy waves to be filtered by an extended duration heating are those of the deepest and narrowest structure that have a frequency approaching the buoyancy frequency. The energetics of the steady state depends only on the spatial and time-integrated properties of the warming. However, the energetics and transient evolution toward a given steady state depend on the temporal properties of the warming and may differ widely.

scholarly journals A Comparison of Compressible and Anelastic Models of Deep Dry Convection

2008 ◽  
Vol 136 (12) ◽  
pp. 4555-4571 ◽  
Author(s):  
Jonathan W. Smith ◽  
Peter R. Bannon
Keyword(s):  
Potential Vorticity ◽  
Acoustic Waves ◽  
Initial Conditions ◽  
Lamb Waves ◽  
Geostrophic Adjustment ◽  
Buoyancy Flow ◽  
Upper Level ◽  
Sponge Layer ◽  
Vertically Propagating ◽  
Dry Convection

Abstract The response to an instantaneous diabatic warming and the resulting hydrostatic and geostrophic adjustment in compressible and anelastic models is examined. The comparison of the models includes examining the initial conditions, time evolution, potential vorticity, and both the traditional and available energetics. Between the two models, the buoyancy flow fields and potential vorticity perturbations are qualitatively and quantitatively similar. Traditional and available energetics can both be accurately conserved within the models. There are some short-lived (e.g., several minutes) differences in the model solutions as the compressible model undergoes an acoustic adjustment that contains vertically propagating acoustic waves and horizontally propagating Lamb waves. The acoustic waves are effectively eliminated in an upper-level numerical sponge layer using Rayleigh damping. Moreover, the relative computational efficiency and accuracy of the two models are assessed.

scholarly journals Nonlinear Atmospheric Adjustment to Thermal Forcing

2005 ◽  
Vol 62 (12) ◽  
pp. 4253-4272 ◽  
Author(s):  
Paul F. Fanelli ◽  
Peter R. Bannon
Keyword(s):  
Steady State ◽  
Potential Energy ◽  
Wave Packet ◽  
Potential Vorticity ◽  
Lamb Wave ◽  
Static Stability ◽  
Lapse Rate ◽  
Thermal Forcing ◽  
The Waves ◽  
Buoyancy Waves

Abstract A nonlinear, numerical model of a compressible atmosphere is used to simulate the hydrostatic and geostrophic adjustment to a localized prescribed heating applied over five minutes with a size characteristic of an isolated, deep, cumulus cloud. This thermal forcing generates both buoyancy waves and a horizontally propagating Lamb wave packet as well as a steady state rich in potential vorticity. The adjustments in three model atmospheres (an isothermal, a constant lapse rate, and one with a stratosphere) are studied. The Lamb wave packet and the two lowest-order buoyancy waves are relatively unaffected by nonlinearities but the higher-order modes and the steady state are. The heating generates a vertically stacked dipole of potential vorticity with a cyclonic perturbation below an anticyclonic perturbation. In contrast to the linear results, the nonlinear dipole is severely distorted by vertical and horizontal advections. In addition, the Lamb wave packet contains some weak positive perturbation potential vorticity. The energetics is examined using traditional and Eulerian available energetics. Traditional energetics consists of kinetic, internal, and potential energies. It is shown that the Lamb wave packet contains more total traditional energy than that input to the atmosphere by the heating. The traditional energy in the packet resides primarily in the form of internal energy and only secondarily in the form of potential energy. The passage of the Lamb wave packet produces an atmosphere that, overall, is cooler, less dense, and with less total traditional energy than the initial atmosphere. Eulerian available energetics consists of kinetic, available potential, and available elastic energies. The heating generates both available elastic and potential energy that is then converted into kinetic energy. Most of the available elastic energy projects onto the Lamb packet, while almost all of the available potential energy is associated with the buoyancy waves and the steady state. The effects of varying the spatial and temporal scale of the heating, while keeping the net heating the same, are examined. As the duration of the heating decreases, the amount of energy projected onto the waves increases. Increasing the size of the heating decreases the amount of energy projected onto the waves. The adjustment is kinetically more vigorous in the nonisothermal atmospheres because of the reduction in the base-state static stability. The presence of a stratosphere produces large anomalies at and above the tropopause that are linked to the vertical motions of the buoyancy wave field.

scholarly journals Wave Response during Hydrostatic and Geostrophic Adjustment. Part I: Transient Dynamics

2005 ◽  
Vol 62 (5) ◽  
pp. 1311-1329 ◽  
Author(s):  
Jeffrey M. Chagnon ◽  
Peter R. Bannon
Keyword(s):  
Acoustic Wave ◽  
Lamb Waves ◽  
Lower Boundary ◽  
Transient Dynamics ◽  
Convective System ◽  
Heated Region ◽  
Geostrophic Adjustment ◽  
Lower Boundary Condition ◽  
Order Of Magnitude ◽  
Buoyancy Waves

Abstract The adjustment of a compressible, stably stratified atmosphere to sources of hydrostatic and geostrophic imbalance is investigated using a linear model. Imbalance is produced by prescribed, time-dependent injections of mass, heat, or momentum that model those processes considered “external” to the scales of motion on which the linearization and other model assumptions are justifiable. Solutions are demonstrated in response to a localized warming characteristic of small isolated clouds, larger thunderstorms, and convective systems. For a semi-infinite atmosphere, solutions consist of a set of vertical modes of continuously varying wavenumber, each of which contains time dependencies classified as steady, acoustic wave, and buoyancy wave contributions. Additionally, a rigid lower-boundary condition implies the existence of a discrete mode—the Lamb mode— containing only a steady and acoustic wave contribution. The forced solutions are generalized in terms of a temporal Green's function, which represents the response to an instantaneous injection. The response to an instantaneous warming with geometry representative of a small, isolated cloud takes place in two stages. Within the first few minutes, acoustic and Lamb waves accomplish an expansion of the heated region. Within the first quarter-hour, nonhydrostatic buoyancy waves accomplish an upward displacement inside of the heated region with inflow below, outflow above, and weak subsidence on the periphery—all mainly accomplished by the lowest vertical wavenumber modes, which have the largest horizontal group speed. More complicated transient patterns of inflow aloft and outflow along the lower boundary are accomplished by higher vertical wavenumber modes. Among these is an outwardly propagating rotor along the lower boundary that effectively displaces the low-level inflow upward and outward. A warming of 20 min duration with geometry representative of a large thunderstorm generates only a weak acoustic response in the horizontal by the Lamb waves. The amplitude of this signal increases during the onset of the heating and decreases as the heating is turned off. The lowest vertical wavenumber buoyancy waves still dominate the horizontal adjustment, and the horizontal scale of displacements is increased by an order of magnitude. Within a few hours the transient motions remove the perturbations and an approximately trivial balanced state is established. A warming of 2 h duration with geometry representative of a large convective system generates a weak but discernible Lamb wave signal. The response to the conglomerate system is mainly hydrostatic. After several hours, the only signal in the vicinity of the heated region is that of inertia–gravity waves oscillating about a nontrivial hydrostatic and geostrophic state. This paper is the first of two parts treating the transient dynamics of hydrostatic and geostrophic adjustment. Part II examines the potential vorticity conservation and the partitioning of total energy.

scholarly journals Adjustment to Injections of Mass, Momentum, and Heat in a Compressible Atmosphere

2005 ◽  
Vol 62 (8) ◽  
pp. 2749-2769 ◽  
Author(s):  
Jeffrey M. Chagnon ◽  
Peter R. Bannon
Keyword(s):  
Steady State ◽  
Acoustic Waves ◽  
Prediction Models ◽  
Weather Prediction ◽  
Short Time Scale ◽  
Mass Source ◽  
Injection Duration ◽  
Wave Response ◽  
Compressible Atmosphere ◽  
Buoyancy Waves

Abstract This study compares the response to injections of mass, heat, and momentum during hydrostatic and geostrophic adjustment in a compressible atmosphere. The sensitivity of the adjustment to these different injection types is examined at varying spatial and temporal scales through analysis of the transient evolution of the fields as well as the partitioning of total energy between acoustic waves, buoyancy waves, Lamb waves, and the steady state. The effect of a cumulus cloud on its larger-scale environment may be represented as a vertical mass source/sink and a localized warming. To examine how the response to such injections may differ, injections of mass and heat that generate identical potential vorticity (PV) distributions and, hence, identical steady states, are compared. When the duration of the injection is very short (e.g., a minute or less), the injection of mass generates a very large acoustic wave response relative to the PV-equivalent injection of heat. However, the buoyancy wave response to these two injection types is quite similar. The responses to injections of divergent momentum in the vertical and horizontal directions are also compared. It is shown that neither divergent momentum injection generates any PV and, thus, there is no steady-state response to these injections. The waves excited by these injections generally propagate their energy in the direction of the injection. Consequently, an injection of vertical momentum is an efficient generator of vertically propagating, horizontally trapped, high-frequency buoyancy waves. Such waves have a short time scale and are therefore very sensitive to the injection duration. Analogously, an injection of divergent horizontal momentum is an efficient generator of horizontally propagating, vertically trapped low-frequency buoyancy waves that are relatively insensitive to the injection duration. Because of this difference in the response to horizontal and vertical injections of momentum, the response to the injection of an isolated updraft differs depending on whether a compensating horizontal inflow/outflow is also specified. This additional specification of inflow/outflow helps filter acoustic waves and encourages a stronger updraft that is not removed as rapidly by the buoyancy waves. This finding is relevant to the initialization of updrafts in compressible numerical weather prediction models. Injection of nondivergent momentum generates waves in the regions of convergence/divergence produced by the deflection of the current by Coriolis forces. The energy partitioning for such an injection is sensitive to the width and depth of the current relative to the Rossby radius of deformation, but the response is insensitive to the duration of injection for time scales shorter than several hours.

scholarly journals Compressive high-frequency waves riding on an Alfvén/ion-cyclotron wave in a multi-fluid plasma

2011 ◽  
Vol 77 (5) ◽  
pp. 693-707 ◽  
Author(s):  
DANIEL VERSCHAREN ◽  
ECKART MARSCH
Keyword(s):  
Acoustic Waves ◽  
High Frequency ◽  
Large Amplitude ◽  
Wave Equations ◽  
Low Frequency ◽  
Plasma Waves ◽  
Alpha Particles ◽  
Alfven Wave ◽  
Resonant Wave ◽  
High Frequency Waves

AbstractIn this paper, we study the weakly-compressive high-frequency plasma waves which are superposed on a large-amplitude Alfvén wave in a multi-fluid plasma consisting of protons, electrons, and alpha particles. For these waves, the plasma environment is inhomogenous due to the presence of the low-frequency Alfvén wave with a large amplitude, a situation that may apply to space plasmas such as the solar corona and solar wind. The dispersion relation of the plasma waves is determined from a linear stability analysis using a new eigenvalue method that is employed to solve the set of differential wave equations which describe the propagation of plasma waves along the direction of the constant component of the Alfvén wave magnetic field. This approach also allows one to consider weak compressive effects. In the presence of the background Alfvén wave, the dispersion branches obtained differ significantly from the situation of a uniform plasma. Due to compressibility, acoustic waves are excited and couplings between various modes occur, and even an instability of the compressive mode. In a kinetic treatment, these plasma waves would be natural candidates for Landau-resonant wave–particle interactions, and may thus via their damping lead to particle heating.

scholarly journals Frequency-domain study of nonthermal gigahertz phonons reveals Fano coupling to charge carriers

2020 ◽  
Vol 6 (51) ◽  
pp. eabd4540
Author(s):  
Thomas Vasileiadis ◽  
Heng Zhang ◽  
Hai Wang ◽  
Mischa Bonn ◽  
George Fytas ◽  
...  
Keyword(s):  
Frequency Domain ◽  
Acoustic Waves ◽  
Lamb Waves ◽  
Charge Carriers ◽  
Acoustic Phonons ◽  
Phonon Spectra ◽  
Electron Hole Plasma ◽  
Nonequilibrium Conditions ◽  
Microelectronic Components ◽  
Anti Stokes

Telecommunication devices exploit hypersonic gigahertz acoustic phonons to mediate signal processing with microwave radiation, and charge carriers to operate various microelectronic components. Potential interactions of hypersound with charge carriers can be revealed through frequency- and momentum-resolved studies of acoustic phonons in photoexcited semiconductors. Here, we present an all-optical method for excitation and frequency-, momentum-, and space-resolved detection of gigahertz acoustic waves in a spatially confined model semiconductor. Lamb waves are excited in a bare silicon membrane using femtosecond optical pulses and detected with frequency-domain micro-Brillouin light spectroscopy. The population of photoexcited gigahertz phonons displays a hundredfold enhancement as compared with thermal equilibrium. The phonon spectra reveal Stokes–anti-Stokes asymmetry due to propagation, and strongly asymmetric Fano resonances due to coupling between the electron-hole plasma and the photoexcited phonons. This work lays the foundation for studying hypersonic signals in nonequilibrium conditions and, more generally, phonon-dependent phenomena in photoexcited nanostructures.

scholarly journals Crack-Length Estimation for Structural Health Monitoring Using the High-Frequency Resonances Excited by the Energy Release during Fatigue-Crack Growth

Sensors ◽  
2021 ◽  
Vol 21 (12) ◽  
pp. 4221
Author(s):  
Roshan Joseph ◽  
Hanfei Mei ◽  
Asaad Migot ◽  
Victor Giurgiutiu
Keyword(s):  
Fatigue Crack ◽  
Fatigue Crack Growth ◽  
Crack Length ◽  
Crack Growth ◽  
Health Monitoring ◽  
Acoustic Waves ◽  
High Frequency ◽  
Fem Analysis ◽  
Signal Frequency ◽  
Propagation Pattern

Acoustic waves are widely used in structural health monitoring (SHM) for detecting fatigue cracking. The strain energy released when a fatigue crack advances has the effect of exciting acoustic waves, which travel through the structures and are picked up by the sensors. Piezoelectric wafer active sensors (PWAS) can effectively sense acoustic waves due to fatigue-crack growth. Conventional acoustic-wave passive SHM, which relies on counting the number of acoustic events, cannot precisely estimate the crack length. In the present research, a novel method for estimating the crack length was proposed based on the high-frequency resonances excited in the crack by the energy released when a crack advances. In this method, a PWAS sensor was used to sense the acoustic wave signal and predict the length of the crack that generated the acoustic event. First, FEM analysis was undertaken of acoustic waves generated due to a fatigue-crack growth event on an aluminum-2024 plate. The FEM analysis was used to predict the wave propagation pattern and the acoustic signal received by the PWAS mounted at a distance of 25 mm from the crack. The analysis was carried out for crack lengths of 4 and 8 mm. The presence of the crack produced scattering of the waves generated at the crack tip; this phenomenon was observable in the wave propagation pattern and in the acoustic signals recorded at the PWAS. A study of the signal frequency spectrum revealed peaks and valleys in the spectrum that changed in frequency and amplitude as the crack length was changed from 4 to 8 mm. The number of peaks and valleys was observed to increase as the crack length increased. We suggest this peak–valley pattern in the signal frequency spectrum can be used to determine the crack length from the acoustic signal alone. An experimental investigation was performed to record the acoustic signals in crack lengths of 4 and 8 mm, and the results were found to match well with the FEM predictions.

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